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By Petersen's theorem, a bridgeless cubic graph has a 2-factor. H. Fleis-chner extended this result to bridgeless graphs of minimum degree at least three by showing that every such graph has a spanning even subgraph. Our main result is that, under the stronger hypothesis of 3-edge-connectivity, we can find a spanning even subgraph in which every component… (More)

By Petersen's theorem, a bridgeless cubic multigraph has a 2-factor. H. Fleischner generalised this result to bridgeless multigraphs of minimum degree at least three by showing that every such multigraph has a spanning even sub-graph. Our main result is that every bridgeless simple graph with minimum degree at least 3 has a spanning even subgraph in which… (More)

Let G be a claw-free graph with order n and minimum degree δ. We improve results of Faudree et al. and Gould & Jacobson, and solve two open problems by proving the following two results. If δ = 4, then G has a 2-factor with at most (5n − 14)/18 components, unless G belongs to a finite class of exceptional graphs. If δ ≥ 5, then G has a 2-factor with at most… (More)

Let k ≥ 2 be an integer. We show that if G is a (k + 1)-connected graph and each pair of nonadjacent vertices in G has degree sum at least |G| + 1, then for each subset S of V (G) with |S| = k, G has a spanning tree such that S is the set of endvertices. This result generalizes Ore's theorem which guarantees the existence of a Hamilton path connecting any… (More)

In this article, we prove that a line graph with minimum degree δ ≥ 7 has a spanning subgraph in which every component is a clique of order at least three. This implies that if G is a line graph with δ ≥ 7, then for any independent set S there is a 2-factor of G such that each cycle contains at most one vertex of S. This supports the conjecture that δ ≥ 5… (More)

- H J Broersma, J Fujisawa, K Yoshimoto, Hajo Broersma, Jun Fujisawa, Kiyoshi Yoshimoto
- 2003

Given a graph G = (V, E) and a spanning subgraph H of G (the backbone of G), a backbone coloring for G and H is a proper vertex coloring V → {1, 2,. . .} of G in which the colors assigned to adjacent vertices in H differ by at least two. In a recent paper, backbone colorings were introduced and studied in cases were the backbone is either a spanning tree or… (More)

- Liming Xiong, Ph D Thesis, Proefschrift Ter, L Xiong, J Wang, Z Li +12 others
- 2001

No part of this work may be reproduced by print, photocopy or any other means without the permission in writing from the publisher. If more distant views are what you desire, you simply have to go up higher. Preface This thesis is the result of almost five years of research in the field of hamiltonian graph theory between September 1996 and April, 2001.… (More)